Abstract This study deals with free, forced undamped vibration and the random, damped vibration of an inhomogeneous beam composed of two materials with significantly different elastic moduli and material densities. Exact solution is obtained for natural frequencies and the mode shapes using Krylov-Duncan functions, along with the comparison with the results furnished by the Galerkin's method. Random vibrations of the bi-material beams are studied for the first time in the literature for the case of proportional damping. Novel element of this study consists in the unintuitive finding that the response of the bi-material beam may considerably exceed the responses of its homogeneous counterparts, composed of a single material. This finding appears of design significance, suggesting that the natural frequencies of the bi-material beam must be made so as to lie above the cutoff frequency of broad-band cutted white noise.

中文翻译：

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由高对比度材料组成的梁的自由、受迫和随机振动

摘要 本研究涉及弹性模量和材料密度明显不同的两种材料组成的非均匀梁的自由、受迫无阻尼振动和随机阻尼振动。使用 Krylov-Duncan 函数获得固有频率和模态振型的精确解，并与 Galerkin 方法提供的结果进行比较。在文献中首次针对比例阻尼情况研究了双材料梁的随机振动。这项研究的新元素在于一个非直观的发现，即双材料梁的响应可能大大超过其由单一材料组成的同质对应物的响应。这一发现似乎具有设计意义，